Now I want to make it clear that I don't have a problem with someone copying another's power. If you can have shape changers then it's not taking it much further to suggest that one character could mimic the structures of another's body that are responsible for the power; say they copied the physical arrangement of Superman's cells that enable him to process light into a form that gives him strength or the ability to fly.
Where I fall down is that I don't see how this process could remove those physical parts from the person's body and replace them with those of a regular human. I know in some cases you could explain it by saying that it's not the physical parts that have been removed, simply that the energy that powers those systems has been drained and so they will not work until the battery is recharged, and the character only assumes that their powers have been "stolen". But even if you drained Superman of all the converted light energy that powers his abilities he should still be Kryptonian and should still be affected by kryptonite. And it does not explain situations where characters have their powers removed permanantly, or are examined and found to be normal humans.
John Byrne does a nice take on this in Fantastic Four #250 where he suggests that it's a hypnotic effect to compliment the mimickery, and the person just believes their powers have been passed on to the other character. Superman's recent depowerment and regaining of those powers is written in a way that suggests the trauma that removed his powers damaged his ability to process sunlight, but that there was also a psychological element. He liked being depowered. He enjoyed being Clark Kent and for a while being free of the huge responsibility of being Superman.